When making PUT request to mycommunity.tribe.so/api/v1/users/:currentUserID and the request JSON body contains the users current email:

email: "current.user.email@mail.com"

we get a 400 bad request error with message: "Email Address is in use".

While it is correct that the Email Address is in use, you should check if the email is the current email of the user before checking if it is in use by other users (email_exists) and only return an error if the email is used by another user. Pseudo-code:

$currentUserEmail = $currentUser->email;
$requestEmail = $_POST['email'];

if ($currentUserEmail !== $requestEmail && email_exists($requestEmail)) {
    return TribeAPIError(
      'Email address is in use.',
      ['status' => 409]

No biggie, but the response code should be 409 (conflict) for this case.